Question: Kevin is 3 times as old as Brandon. Fifteen years ago, Kevin was 8 times as old as Brandon. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Brandon. Let Kevin's current age be $k$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $k = 3b$ Fifteen years ago, Kevin was $k - 15$ years old, and Brandon was $b - 15$ years old. The information in the second sentence can be expressed in the following equation: $k - 15 = 8(b - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = k / 3$ . Substituting this into our second equation, we get: $k - 15 = 8($ $(k / 3)$ $- 15)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 15 = \dfrac{8}{3} k - 120$ Solving for $k$ , we get: $\dfrac{5}{3} k = 105$ $k = \dfrac{3}{5} \cdot 105 = 63$.